Obtaining Fuzzy Membership Function of Clusters With the Memristor Hardware Implementation and On-Chip Learning

In this paper, we introduce a memristor-crossbar based hardware in order to implement the Clustering Fuzzification Algorithm with on-chip learning capability. The proposed Clustering Fuzzification Algorithm (CFA) is able to fuzzify all crisp clusters and obtain the fuzzy membership functions based on the density of the clusters. Fuzzy clustering is a more natural way of clustering than hard clustering, which is more similar to the way of categorizing by the human brain. However, there are various crisp algorithms with different capabilities to deal with different clustering problems. By means of CFA, it is possible to benefit from the diversity of crisp clustering algorithms and the advantages of having fuzzy clusters simultaneously. According to the high computational complexity of CFA, utilizing an analog structure of real-time processing can be beneficial. Recently, implementation of neural networks and fuzzy algorithms on memristive devices has emerged in the machine learning field. In this research, in order to take advantages of the memristor devices as the valuable analog structure, the clustering fuzzification algorithm is adapted with the concepts of processing in the memristor-crossbar structure, and an implementation of the algorithm on the memristor-crossbar structure is introduced. Computer simulations confirmed the precision of the implemented algorithm.